An Analytical Approach to the Nonlinear Dynamics of Moist Frontogenesis

Abstract

The existence of analytical solutions for two-dimensional nonlinear semigeostrophic models of moist frontogenesis is investigated. Two different schemes for the modeling of stratiform cloud thermodynamics are taken into account, one based on the assumption of an everywhere cloudy environment, while in the other the atmosphere is considered to be exactly saturated and only condensation effects are relevant. In the first case, an exact analytical solution is derived for arbitrary boundary conditions, which satisfies the requirements for the validation of the semigeostrophic approximation even when the atmosphere is conditionally unstable with respect to slantwise convection. The growth of symmetric instabilities with no short-wave cutoff is predicted for this conditionally unstable atmosphere, even under the approximations of the semigeostrophic theory. An analogous, but approximate, analytical solution is then proposed for the second case. The errors introduced by the approximation are, however, not bigger than the terms neglected in the semigeostrophic approximation itself.